Sampling variance of flood quantiles from the generalised logistic distribution estimated using the method of L-moments

Abstract. The method of L-moments is the recommended method for fitting the three parameters (location, scale and shape) of a Generalised Logistic (GLO) distribution when conducting flood frequency analyses in the UK. This paper examines the sampling uncertainty of quantile estimates obtained using the GLO distribution for single site analysis using the median to estimate the location parameter. Analytical expressions for the mean and variance of the quantile estimates were derived, based on asymptotic theory. This has involved deriving expressions for the covariance between the sampling median (location parameter) and the quantiles of the estimated unit-median GLO distribution (growth curve). The accuracy of the asymptotic approximations for many of these intermediate results and for the quantile estimates was investigated by comparing the approximations to the outcome of a series of Monte Carlo experiments. The approximations were found to be adequate for GLO shape parameter values between –0.35 and 0.25, which is an interval that includes the shape parameter estimates for most British catchments. An investigation into the contribution of different components to the total uncertainty showed that for large returns periods, the variance of the growth curve is larger than the contribution of the median. Therefore, statistical methods using regional information to estimate the growth curve should be considered when estimating design events at large return periods.

Keywords: flood frequency analysis, Flood Estimation Handbook, single site, annual maximum series, Generalised Logistic Distribution, uncertainty